Dubrovin-Novikov type Poisson brackets (DN-brackets)
type: Item
instance of: scholarly article
title: Dubrovin-Novikov type Poisson brackets (DN-brackets)
zbMATH Open document ID: 0671.58006
DOI: 10.1007/BF01077434
publication date: 1988-01-01T00:00:00Z
review text: The paper is concerned with canonical forms of the Poisson bracket \[ \{u^ i(x),u^ j(y)\}=\sum g^{ij\alpha}(u(x))\partial \delta (x- y)/\partial x^{\alpha}+\sum (\partial u^ k(x\quad)/\partial x^{\alpha})b_ k^{ij\alpha}(u(x))\delta (x-y) \] of hydrodynamical type (where \(g^{ij\alpha}(u)\), \(u(u^ 1,...,u^ N)\), are nondegenerate metric tensors, \(b_ k^{ij\alpha}=\sum g^{is\alpha} \Gamma^{j\alpha}_{sk}\), and the symmetric connections \(\Gamma^{j\alpha}_{ik}\) related to the metrics are of zero curvature) correcting some previous results presented in several other articles.
Mathematics Subject Classification ID: 58A99
Mathematics Subject Classification ID: 58B99
zbMATH DE Number: 4098330
zbMATH Keywords: canonical form
zbMATH Keywords: Poisson bracket
zbMATH Keywords: symmetric connections
author: O. I. Mokhov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01077434
OpenAlex ID: W2033251586
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4098330